Could you tell me whether there are tools available (I expect such
in XGAP) for grafical displaying of the graph of the group (group
diagram) ? I mean graph which is introduced at the end of the 1st
chapter of "Combinatorial Group Theory" by Magnus-Carrass-Solitar.

Unfortunately the answer is negative. XGAP does not provide the
possibility to display (Cayley-) graphs of groups at present.

While it is fairly easy to write a program using XGAP that will
display *undirected* graphs from their adjacency matrix (and in fact
such a programm has been written by Max Neunhoeffer for private use),
to write a program to display *directed* graphs would need the
extension of basic facilities of XGAP, namely the introduction of
'directed edges' as new basic graphical objects. This is possible, but
would mean a somewhat larger piece of work which we do not have
manpower to provide in the nearer future. Since the introduction of
such a new object 'directed edge' into XGAP would need changes and
extensions embedded rather deeply in XGAP, we think that also
unfortunately we cannot encourage to attempt such a change yourself.

We will, however, put this request on the (long!) list of desiderata
and possible projects for GAP.